Ryo Takahashi

Graduate School of Mathematics
Nagoya University
Furocho, Chikusaku, Nagoya 464-8602, Japan

Papers

  1. Powers of the maximal ideal and vanishing of (co)homology (with Olgur Celikbas)
    Glasg. Math. J. (to appear).

  2. Generation in singularity categories of hypersurfaces of countable representation type (with Tokuji Araya, Kei-ichiro Iima and Maiko Ono)
    Arch. Math. (Basel) (to appear).

  3. Little dimension and the improved new intersection theorem (with Tsutomu Nakamura and Siamak Yassemi)
    Math. Scand. (to appear).

  4. Local rings with quasi-decomposable maximal ideal (with Saeed Nasseh)
    Math. Proc. Cambridge Philos. Soc. (to appear).

  5. The Jacobian ideal of a commutative ring and annihilators of cohomology (with Srikanth B. Iyengar)
    J. Algebra (to appear), Special issue dedicated to Craig Huneke.

  6. Homogeneous prime elements in normal two-dimensional graded rings (with Anurag K. Singh and Kei-ichi Watanabe)
    J. Algebra (to appear), Special issue dedicated to Craig Huneke.

  7. Rings whose ideals are isomorphic to trace ideals (with Toshinori Kobayashi)
    Math. Nachr. 292 (2019), no. 10, 2252--2261.

  8. Associated primes and syzygies of linked modules (with Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi and Arash Sadeghi)
    J. Commut. Algebra 11 (2019), no. 3, 301--323.

  9. Two generalizations of Auslander-Reiten duality and applications (with Arash Sadeghi)
    Illinois J. Math. 63 (2019), no. 2, 335--351.

  10. Ulrich modules over Cohen-Macaulay local rings with minimal multiplicity (with Toshinori Kobayashi)
    Q. J. Math. 70 (2019), no. 2, 487--507.

  11. On the ideal case of a conjecture of Huneke and Wiegand (with Olgur Celikbas, Shiro Goto and Naoki Taniguchi)
    Proc. Edinb. Math. Soc. (2) 62 (2019), no. 3, 847--859.

  12. On the second rigidity theorem of Huneke and Wiegand (with Olgur Celikbas)
    Proc. Amer. Math. Soc. 147 (2019), no. 7, 2733--2739.

  13. On the transitivity of degeneration of modules
    Manuscripta Math. 159 (2019), no. 3, 431--444.

  14. Openness of the regular locus and generators for module categories (with Srikanth B. Iyengar)
    Acta Math. Vietnam. 44 (2019), no. 1, 207--212, Special issue: The prospects for Commutative Algebra.

  15. Noncommutative resolutions using syzygies (with Hailong Dao, Osamu Iyama, Srikanth B. Iyengar, Michael Wemyss and Yuji Yoshino)
    Bull. Lond. Math. Soc. 51 (2019), no. 1, 43--48.

  16. Degenerations over (A)-singularities and construction of degenerations over commutative rings (with Naoya Hiramatsu and Yuji Yoshino)
    J. Algebra 525 (2019), 374--389.

  17. Remarks on dimensions of triangulated categories (with Takuma Aihara)
    J. Algebra 521 (2019), 235--246.

  18. Totally reflexive modules and Poincaré series (with Mohsen Gheibi)
    J. Algebra 520 (2019), 440--459.

  19. Applications and homological properties of local rings with decomposable maximal ideals (with Saeed Nasseh, Sean Sather-Wagstaff and Keller VandeBogert)
    J. Pure Appl. Algebra 223 (2019), no. 3, 1272--1287.

  20. On the vanishing of self extensions over Cohen-Macaulay local rings (with Tokuji Araya, Olgur Celikbas and Arash Sadeghi)
    Proc. Amer. Math. Soc. 146 (2018), no. 11, 4563--4570.

  21. Structure of irreducible homomorphisms to/from free modules (with Saeed Nasseh)
    Algebr. Represent. Theory 21 (2018), no. 2, 471--485.

  22. On the ideal case of a conjecture of Auslander and Reiten (with Olgur Celikbas, Kei-ichiro Iima and Arash Sadeghi)
    Bull. Sci. Math. 142 (2018), 94--107.

  23. Thick tensor ideals of right bounded derived categories (with Hiroki Matsui)
    Algebra Number Theory 11 (2017), no. 7, 1677--1738.

  24. Thick subcategories over isolated singularities
    Pacific J. Math. 291 (2017), no. 1, 183--211.

  25. On the Auslander-Reiten conjecture for Cohen-Macaulay local rings (with Shiro Goto)
    Proc. Amer. Math. Soc. 145 (2017), no. 8, 3289--3296.

  26. When are n-syzygy modules n-torsionfree? (with Hiroki Matsui and Yoshinao Tsuchiya)
    Arch. Math. (Basel) 108 (2017), no. 4, 351--355.

  27. Singularity categories and singular equivalences for resolving subcategories (with Hiroki Matsui)
    Math. Z. 285 (2017), no. 1, 251--286.

  28. Annihilation of cohomology, generation of modules and finiteness of derived dimension (with Abdolnaser Bahlekeh, Ehsan Hakimian and Shokrollah Salarian)
    Q. J. Math. 67 (2016), no. 3, 387--404.

  29. Ulrich ideals and modules over two-dimensional rational singularities (with Shiro Goto, Kazuho Ozeki, Kei-ichi Watanabe and Ken-ichi Yoshida)
    Nagoya Math. J. 221 (2016), no. 1, 69--110.

  30. Extension closedness of syzygies and local Gorensteinness of commutative rings (with Shiro Goto)
    Algebr. Represent. Theory 19 (2016), no. 3, 511--521.

  31. Perfect linkage of Cohen-Macaulay modules over Cohen-Macaulay rings (with Kei-ichiro Iima)
    J. Algebra 458 (2016), 134--155.

  32. Annihilation of cohomology and strong generation of module categories (with Srikanth B. Iyengar)
    Int. Math. Res. Not. IMRN (2016), no. 2, 499--535.

  33. Ulrich ideals and almost Gorenstein rings (with Shiro Goto and Naoki Taniguchi)
    Proc. Amer. Math. Soc. 144 (2016), no. 7, 2811--2823.

  34. The dimension of a subcategory of modules (with Hailong Dao)
    Forum Math. Sigma 3 (2015), e19, 31 pp.

  35. Generators and dimensions of derived categories of modules (with Takuma Aihara)
    Comm. Algebra 43 (2015), no. 11, 5003--5029.

  36. Endofunctors of singularity categories characterizing Gorenstein rings (with Takuma Aihara)
    Proc. Amer. Math. Soc. 143 (2015), no. 9, 3777--3779.

  37. Classification of resolving subcategories and grade consistent functions (with Hailong Dao)
    Int. Math. Res. Not. IMRN (2015), no. 1, 119--149.

  38. Non-commutative resolutions and Grothendieck groups (with Hailong Dao, Osamu Iyama and Charles Vial)
    J. Noncommut. Geom. 9 (2015), no. 1, 21--34.

  39. Maximal Cohen-Macaulay approximations and Serre's condition (with Hiroki Matsui)
    Acta Math. Vietnam. 40 (2015), no. 1, 197--203, Special Issue: Commutative Algebra and its Interaction with Algebraic Geometry and Combinatorics.

  40. Building modules from the singular locus (with Jesse Burke and Lars Winther Christensen)
    Math. Scand. 116 (2015), no. 1, 23--33.

  41. Upper bounds for dimensions of singularity categories (with Hailong Dao)
    C. R. Math. Acad. Sci. Paris 353 (2015), no. 4, 297--301.

  42. Almost Gorenstein rings -- towards a theory of higher dimension -- (with Shiro Goto and Naoki Taniguchi)
    J. Pure Appl. Algebra 219 (2015), no. 7, 2666--2712.

  43. Bounds on depth of tensor products of modules (with Olgur Celikbas and Arash Sadeghi)
    J. Pure Appl. Algebra 219 (2015), no. 5, 1670--1684.

  44. Huneke-Wiegand conjecture and change of rings (with Shiro Goto, Naoki Taniguchi and Hoang Le Truong)
    J. Algebra 422 (2015), 33--52.

  45. Annihilation of cohomology and decompositions of derived categories (with Srikanth B. Iyengar)
    Homology, Homotopy Appl. 16 (2014), no. 2, 231--237.

  46. Brauer-Thrall for totally reflexive modules over local rings of higher dimension (with Olgur Celikbas and Mohsen Gheibi)
    Algebr. Represent. Theory 17 (2014), no. 3, 997--1008.

  47. Modules that detect finite homological dimensions (with Olgur Celikbas and Hailong Dao)
    Kyoto J. Math. 54 (2014), no. 2, 295--310.

  48. Reconstruction from Koszul homology and applications to module and derived categories
    Pacific J. Math. 268 (2014), no. 1, 231--248.

  49. The radius of a subcategory of modules (with Hailong Dao)
    Algebra Number Theory 8 (2014), no. 1, 141--172.

  50. Dimensions of triangulated categories with respect to subcategories (with Takuma Aihara, Tokuji Araya, Osamu Iyama and Michio Yoshiwaki)
    J. Algebra 399 (2014), 205--219.

  51. Ulrich ideals and modules (with Shiro Goto, Kazuho Ozeki, Kei-ichi Watanabe and Ken-ichi Yoshida)
    Math. Proc. Cambridge Philos. Soc. 156 (2014), no. 1, 137--166.

  52. Tilting and cluster tilting for quotient singularities (with Osamu Iyama)
    Math. Ann. 356 (2013), no. 3, 1065--1105.

  53. Thick subcategories over Gorenstein local rings that are locally hypersurfaces on the punctured spectra
    J. Math. Soc. Japan 65 (2013), no. 2, 357--374.

  54. Auslander-Reiten conjecture and Auslander-Reiten duality (with Olgur Celikbas)
    J. Algebra 382 (2013), 100--114.

  55. Classifying resolving subcategories over a Cohen-Macaulay local ring
    Math. Z. 273 (2013), no. 1, 569--587.

  56. On the left perpendicular category of the modules of finite projective dimension (with Tokuji Araya and Kei-ichiro Iima)
    Comm. Algebra 40 (2012), no. 8, 2693--2699.

  57. On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type (with Tokuji Araya and Kei-ichiro Iima)
    J. Algebra 361 (2012), 213--224.

  58. Contravariantly finite resolving subcategories over commutative rings
    Amer. J. Math. 133 (2011), no. 2, 417--436.

  59. When is there a nontrivial extension-closed subcategory?
    J. Algebra 331 (2011), no. 1, 388--399.

  60. Classifying thick subcategories of the stable category of Cohen-Macaulay modules
    Adv. Math. 225 (2010), no. 4, 2076--2116.

  61. On the existence of embeddings into modules of finite homological dimensions (with Siamak Yassemi and Yuji Yoshino)
    Proc. Amer. Math. Soc. 138 (2010), no. 7, 2265--2268.

  62. Homological aspects of semidualizing modules (with Diana White)
    Math. Scand. 106 (2010), no. 1, 5--22.

  63. On localizing subcategories of derived categories
    J. Math. Kyoto Univ. 49 (2009), no. 4, 771--783.

  64. A generalization of a theorem of Foxby (with Tokuji Araya)
    Arch. Math. (Basel) 93 (2009), no. 2, 123--127.

  65. Modules in resolving subcategories which are free on the punctured spectrum
    Pacific J. Math. 241 (2009), no. 2, 347--367.

  66. Local cohomology based on a nonclosed support defined by a pair of ideals (with Yuji Yoshino and Takeshi Yoshizawa)
    J. Pure Appl. Algebra 213 (2009), no. 4, 582--600.

  67. On G-regular local rings
    Comm. Algebra 36 (2008), no.12, 4472--4491.

  68. On vanishing of certain Ext modules (with Shiro Goto and Futoshi Hayasaka)
    J. Math. Soc. Japan 60 (2008), no. 4, 1045--1064.

  69. Classifying subcategories of modules over a commutative noetherian ring
    J. Lond. Math. Soc. (2) 78 (2008), no. 3, 767--782.

  70. Finite Gorenstein representation type implies simple singularity (with Lars Winther Christensen, Greg Piepmeyer and Janet Striuli)
    Adv. Math. 218 (2008), no. 4, 1012--1026.

  71. D-modules over rings with finite F-representation type (with Shunsuke Takagi)
    Math. Res. Lett. 15 (2008), no. 3, 563--581.

  72. Direct summands of syzygy modules of the residue class field
    Nagoya Math. J. 189 (2008), 1--25.

  73. Quasi-socle ideals in a Gorenstein local ring (with Shiro Goto and Naoyuki Matsuoka)
    J. Pure Appl. Algebra 212 (2008), no. 5, 969--980.

  74. An uncountably infinite number of indecomposable totally reflexive modules
    Nagoya Math. J. 187 (2007), 35--48.

  75. A characterization of modules locally of finite injective dimension
    Proc. Amer. Math. Soc. 135 (2007), no. 11, 3461--3464.

  76. On the number of indecomposable totally reflexive modules
    Bull. London Math. Soc. 39 (2007), no. 3, 487--492.

  77. Totally reflexive modules constructed from smooth projective curves of genus g >= 2 (with Kei-ichi Watanabe)
    Arch. Math. (Basel) 89 (2007), no. 1, 60--67.

  78. A new approximation theory which unifies spherical and Cohen-Macaulay approximations
    J. Pure Appl. Algebra 208 (2007), no. 2, 617--634.

  79. Openness of FID-loci
    Glasg. Math. J. 48 (2006), no. 3, 431--435.

  80. Remarks on modules approximated by G-projective modules
    J. Algebra 301 (2006), no. 2, 748--780.

  81. The existence of finitely generated modules of finite Gorenstein injective dimension
    Proc. Amer. Math. Soc. 134 (2006), no. 11, 3115--3121.

  82. A note on a theorem of F. Wang and G. Tang
    Bull. Austral. Math. Soc. 73 (2006), 293--297.

  83. Syzygy modules with semidualizing or G-projective summands
    J. Algebra 295 (2006), no. 1, 179--194.

  84. On the category of modules of Gorenstein dimension zero
    Math. Z. 251 (2005), no. 2, 249--256.

  85. Homological invariants associated to semi-dualizing bimodules (with Tokuji Araya and Yuji Yoshino)
    J. Math. Kyoto Univ. 45 (2005), no. 2, 287--306.

  86. Modules of G-dimension zero over local rings of depth two
    Illinois J. Math. 48 (2004), no. 3, 945--952.

  87. Upper Cohen-Macaulay dimension (with Tokuji Araya and Yuji Yoshino)
    Math. J. Okayama Univ. 46 (2004), 17--30.

  88. Some characterizations of Gorenstein local rings in terms of G-dimension
    Acta Math. Hungar. 104 (2004), no. 4, 315--322.

  89. Characterizing Cohen-Macaulay local rings by Frobenius maps (with Yuji Yoshino)
    Proc. Amer. Math. Soc. 132 (2004), no. 11, 3177--3187.

  90. On the category of modules of Gorenstein dimension zero II
    J. Algebra 278 (2004), no. 1, 402--410.

  91. Upper complete intersection dimension relative to a local homomorphism
    Tokyo J. Math. 27 (2004), no. 1, 209--219.

  92. Nagata criterion for Serre's (Rn) and (Sn)-conditions
    Math. J. Okayama Univ. 41 (1999), 37--43 (2001).